Finite Group Databasebeta

← C2×#22592466 #32165030

Subgroups — C2×#22592466 #32165030

Order 18176.

4946 conjugacy classes of subgroups.

The subgroup lattice has 1004 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556116C211yesmaximal, characteristic, complemented
2C22×#14556105C211yesmaximal, characteristic, complemented
3C22×#14556098C211yesmaximal, characteristic
4C23×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
5#22592466C2116yesmaximal, direct product factor
6C2×#17985926C211yesmaximal, characteristic, complemented
7C2×#17985917C211yesmaximal, characteristic, complemented
8C2×#17985917C211yesmaximal, characteristic, complemented
9C2×#17985912C211yesmaximal, characteristic, complemented
10C2×#17985901C211yesmaximal, characteristic, complemented
11C2×#17985890C211yesmaximal, characteristic, complemented
12C2×#17985890C211yesmaximal, characteristic, complemented
13C2×#17985878C211yesmaximal, characteristic, complemented
14C2×#17985876C211yesmaximal, characteristic, complemented
15C2×#17985854C211yesmaximal, characteristic, complemented
16C2×C4×C22⋊C4×C71C211yesmaximal, characteristic, complemented
17C25×D71C2211yescharacteristic
18C23×Dic142C2211yescharacteristic, complemented
19C23×D284C2211yescharacteristic
20C23×D284C2211yescharacteristic
21C23×C22⋊D71C2211yescharacteristic
22C24×Dic71C2211yescharacteristic
23C2×#14556116—28no—
24C2×#14556116C2218yescomplemented
25C2×#14556105—28no—
26C2×#14556105C2218yescomplemented
27C2×#14556098—28no—
28C2×#14556098C2218yes—
29C22×C4⋊Dic71C2211yescharacteristic, complemented
30C22×Dic71⋊C4C2211yescharacteristic, complemented
31C22×Dic71⋊C4C2211yescharacteristic, complemented
32C22×C22⋊Dic71C2211yescharacteristic
33C22×(C2×D71)⋊C4—28no—
34C22×(C2×D71)⋊C4C2211yescharacteristic
35C22×(C2×D71)⋊C4C2211yescharacteristic
36C22×(C2×D71)⋊C4C2211yescharacteristic
37C22×(C2×D71)⋊C4C2211yescharacteristic
38C22×(C2×D71)⋊C4C2211yescharacteristic
39C22×(C2×D71)⋊C4C2211yescharacteristic
40C22×(C2×D71)⋊C4C2211yescharacteristic
41C22×(C2×D71)⋊C4C2211yescharacteristic
42C22×(C2×D71)⋊C4C2211yescharacteristic
43C22×(C2×D71)⋊C4C2211yescharacteristic
44C22×(C2×D71)⋊C4C2218yescomplemented
45C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
46C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
47C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
48C22×(C2×D71)⋊C4C2211yescharacteristic, complemented
49#17985926C2218yescomplemented
50#17985917C2218yescomplemented
51#17985917C2218yescomplemented
52#17985912C2218yescomplemented
53#17985901C2218yescomplemented
54#17985890C2218yescomplemented
55#17985890C2218yescomplemented
56#17985878C2218yescomplemented
57#17985876C2218yescomplemented
58#17985854C2218yescomplemented
59C2×C71⋊#95C2211yescharacteristic, complemented
60C2×C71⋊#95C2211yescharacteristic, complemented
61C2×C71⋊#95C2211yescharacteristic, complemented
62C2×C71⋊#95C2211yescharacteristic, complemented
63C24×C4×C71C2211yescharacteristic
64C22×C22⋊C4×C71C2211yescharacteristic
65C22×C22⋊C4×C71C2211yescharacteristic
66C22×C42×C71C2211yescharacteristic, complemented
67C22×C42×C71C2211yescharacteristic, complemented
68C4×C22⋊C4×C71C2218yescomplemented
69C2×#95×C71C2211yescharacteristic, complemented
70C2×#95×C71C2211yescharacteristic, complemented
71C24×D71—24no—
72C24×D71—24no—
73C24×D71—24no—
74C24×D71—24no—
75C24×D71—24no—
76C24×D71—42no—
77C24×D71—42no—
78C24×D71C2311yescharacteristic
79C24×D71C2311yescharacteristic
80C24×D71C2311yescharacteristic
81C24×D71C2314yes—
82C22×Dic142—24no—
83C22×Dic142—24no—
84C22×Dic142—42no—
85C22×Dic142C2314yescomplemented
86C22×D284—24no—
87C22×D284—24no—
88C22×D284—24no—
89C22×D284—24no—
90C22×D284—42no—
91C22×D284—42no—
92C22×D284C2314yes—
93C22×D284C2314yes—
94C22×C22⋊D71—24no—
95C22×C22⋊D71—24no—
96C22×C22⋊D71—24no—
97C22×C22⋊D71C2314yes—
98C23×Dic71—24no—
99C23×Dic71—24no—
100C23×Dic71—42no—
101C23×Dic71C2311yescharacteristic
102C23×Dic71C2311yescharacteristic
103C23×Dic71C2311yescharacteristic
104C23×Dic71C2311yescharacteristic
105C23×Dic71C2314yes—
106C23×Dic71C2311yescharacteristic
107#14556116—232no—
108#14556105—232no—
109#14556098—232no—
110C2×C4⋊Dic71—24no—
111C2×C4⋊Dic71C2314yescomplemented
112C2×Dic71⋊C4—24no—
113C2×Dic71⋊C4—24no—
114C2×Dic71⋊C4C2314yescomplemented
115C2×Dic71⋊C4C2314yescomplemented
116C2×C22⋊Dic71—24no—
117C2×C22⋊Dic71C2314yes—
118C2×(C2×D71)⋊C4—24no—
119C2×(C2×D71)⋊C4—24no—
120C2×(C2×D71)⋊C4—24no—
121C2×(C2×D71)⋊C4—24no—
122C2×(C2×D71)⋊C4—24no—
123C2×(C2×D71)⋊C4—232no—
124C2×(C2×D71)⋊C4—24no—
125C2×(C2×D71)⋊C4—24no—
126C2×(C2×D71)⋊C4—24no—
127C2×(C2×D71)⋊C4—24no—
128C2×(C2×D71)⋊C4—42no—
129C2×(C2×D71)⋊C4—42no—
130C2×(C2×D71)⋊C4—42no—
131C2×(C2×D71)⋊C4—42no—
132C2×(C2×D71)⋊C4D418yescomplemented
133C2×(C2×D71)⋊C4C2314yes—
134C2×(C2×D71)⋊C4C2314yes—
135C2×(C2×D71)⋊C4C2314yes—
136C2×(C2×D71)⋊C4C2314yes—
137C2×(C2×D71)⋊C4C2314yes—
138C2×(C2×D71)⋊C4C2314yes—
139C2×(C2×D71)⋊C4C2314yes—
140C2×(C2×D71)⋊C4C2314yes—
141C2×(C2×D71)⋊C4C2314yes—
142C2×(C2×D71)⋊C4C2314yes—
143C2×(C2×D71)⋊C4C2314yescomplemented
144C2×(C2×D71)⋊C4C2314yescomplemented
145C2×(C2×D71)⋊C4C2314yescomplemented
146C2×(C2×D71)⋊C4C2314yescomplemented
147C71⋊#95C2314yescomplemented
148C71⋊#95C2314yescomplemented
149C71⋊#95C2314yescomplemented
150C71⋊#95C2314yescomplemented
151C25×C71C2311yescharacteristic
152C23×C4×C71—24no—
153C23×C4×C71—24no—
154C23×C4×C71—42no—
155C23×C4×C71C2311yescharacteristic
156C23×C4×C71C2311yescharacteristic
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2314yes—
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C23×C4×C71C2311yescharacteristic
162C2×C22⋊C4×C71—24no—
163C2×C22⋊C4×C71D418yes—
164C2×C22⋊C4×C71C2314yes—
165C2×C22⋊C4×C71C2314yes—
166C2×C42×C71—24no—
167C2×C42×C71—42no—
168C2×C42×C71C2314yescomplemented
169C2×C42×C71C2314yescomplemented
170#95×C71C2314yescomplemented
171#95×C71C2314yescomplemented
172C23×D71—232no—
173C23×D71—22no—
174C23×D71—22no—
175C23×D71—22no—
176C23×D71—22no—
177C23×D71—28no—
178C23×D71—22no—
179C23×D71—22no—
180C23×D71—22no—
181C23×D71—22no—
182C23×D71—22no—
183C23×D71—22no—
184C23×D71—22no—
185C23×D71—22no—
186C23×D71—28no—
187C23×D71—28no—
188C23×D71—22no—
189C23×D71—22no—
190C23×D71—28no—
191C23×D71—22no—
192C23×D71—22no—
193C23×D71—22no—
194C23×D71—28no—
195C23×D71—22no—
196C23×D71—22no—
197C23×D71—44no—
198C23×D71—44no—
199C23×D71—416no—
200C23×D71—416no—
201C23×D71—416no—
202C23×D71—416no—
203C23×D71—416no—
204C23×D71—416no—
205C23×D71C2×D414yes—
206C23×D71#4114yes—
207C23×D71C2412yes—
208C23×D71C2412yes—
209C23×D71C2412yes—
210C2×Dic142—28no—
211C2×Dic142—28no—
212C2×Dic142—44no—
213C2×Dic142—416no—
214C2×D284—28no—
215C2×D284—28no—
216C2×D284—28no—
217C2×D284—28no—
218C2×D284—44no—
219C2×D284—44no—
220C2×D284—416no—
221C2×D284—416no—
222C2×C22⋊D71—28no—
223C2×C22⋊D71—28no—
224C2×C22⋊D71—28no—
225C2×C22⋊D71—416no—
226C22×Dic71—22no—
227C22×Dic71—22no—
228C22×Dic71—22no—
229C22×Dic71—22no—
230C22×Dic71—28no—
231C22×Dic71—22no—
232C22×Dic71—22no—
233C22×Dic71—22no—
234C22×Dic71—22no—
235C22×Dic71—22no—
236C22×Dic71—22no—
237C22×Dic71—22no—
238C22×Dic71—22no—
239C22×Dic71—22no—
240C22×Dic71—22no—
241C22×Dic71—28no—
242C22×Dic71—44no—
243C22×Dic71—416no—
244C22×Dic71C2×D414yes—
245C22×Dic71C2412yes—
246C22×Dic71C2412yes—
247C22×Dic71C2412yes—
248C22×Dic71C2412yes—
249C22×Dic71C2412yes—
250C4⋊Dic71—28no—
251Dic71⋊C4—28no—
252Dic71⋊C4—28no—
253C22⋊Dic71—28no—
254(C2×D71)⋊C4—28no—
255(C2×D71)⋊C4—28no—
256(C2×D71)⋊C4—28no—
257(C2×D71)⋊C4—28no—
258(C2×D71)⋊C4—28no—
259(C2×D71)⋊C4—28no—
260(C2×D71)⋊C4—28no—
261(C2×D71)⋊C4—28no—
262(C2×D71)⋊C4—28no—
263(C2×D71)⋊C4—44no—
264(C2×D71)⋊C4—44no—
265(C2×D71)⋊C4—44no—
266(C2×D71)⋊C4—44no—
267(C2×D71)⋊C4C2×D4116yescomplemented
268C24×C71—22no—
269C24×C71—22no—
270C24×C71—22no—
271C24×C71—22no—
272C24×C71C2×D414yes—
273C24×C71#4114yes—
274C24×C71#4114yes—
275C24×C71C2412yes—
276C24×C71C2411yescharacteristic
277C22×C4×C71—22no—
278C22×C4×C71—22no—
279C22×C4×C71—22no—
280C22×C4×C71—22no—
281C22×C4×C71—22no—
282C22×C4×C71—22no—
283C22×C4×C71—22no—
284C22×C4×C71—22no—
285C22×C4×C71—22no—
286C22×C4×C71—22no—
287C22×C4×C71—28no—
288C22×C4×C71—22no—
289C22×C4×C71—22no—
290C22×C4×C71—22no—
291C22×C4×C71—22no—
292C22×C4×C71—22no—
293C22×C4×C71—28no—
294C22×C4×C71—44no—
295C22×C4×C71—416no—
296C22×C4×C71C2×D414yes—
297C22×C4×C71C2×D414yes—
298C22×C4×C71C2×D414yes—
299C22×C4×C71C2412yes—
300C22×C4×C71C2412yes—
301C22×C4×C71C2412yes—
302C22×C4×C71C2412yes—
303C22×C4×C71C2412yes—
304C22×C4×C71C2412yes—
305C22⋊C4×C71—28no—
306C22⋊C4×C71C2×D4116yes—
307C42×C71—28no—
308C42×C71—44no—
309C23×C71—28no—
310C23×C71—28no—
311C23×C71—28no—
312C23×C71—28no—
313C23×C71—28no—
314C23×C71—28no—
315C23×C71—22no—
316C23×C71—22no—
317C23×C71—22no—
318C23×C71—22no—
319C23×C71#124116yescomplemented
320C23×C71C22×D412yes—
321C23×C71C22×D414yes—
322C23×C71C22×D412yes—
323C23×C71C2×#4112yes—
324C23×C71C2×#4114yes—
325C23×C71C2×#4114yes—
326C23×C71C2×#4112yes—
327C23×C71C2×#4112yes—
328C23×C71H(5,𝔽2)12yes—
329C23×C71H(5,𝔽2)12yes—
330C23×C71C2511yescharacteristic
331C22×D71—232no—
332C22×D71—28no—
333C22×D71—28no—
334C22×D71—28no—
335C22×D71—28no—
336C22×D71—28no—
337C22×D71—28no—
338C22×D71—22no—
339C22×D71—22no—
340C22×D71—22no—
341C22×D71—22no—
342C22×D71—22no—
343C22×D71—22no—
344C22×D71—22no—
345C22×D71—22no—
346C22×D71—22no—
347C22×D71—22no—
348C22×D71—22no—
349C22×D71—22no—
350C22×D71—22no—
351C22×D71—22no—
352C22×D71—22no—
353C22×D71—22no—
354C22×D71—22no—
355C22×D71—22no—
356C22×D71—22no—
357C22×D71—416no—
358C22×D71—416no—
359C22×D71—416no—
360C22×D71—416no—
361C22×D71—416no—
362C22×D71—4128no—
363C22×D71—44no—
364C22×D71—44no—
365C22×D71—416no—
366C22×D71—44no—
367C22×D71—44no—
368C22×D71—44no—
369C22×D71—44no—
370C22×D71—44no—
371C22×D71—44no—
372C22×D71—44no—
373C22×D71—44no—
374C22×D71—44no—
375C22×D71—44no—
376C22×D71—44no—
377C22×D71—44no—
378C22×D71—44no—
379C22×D71C22×D414yes—
380C22×D71C2×#4114yes—
381C2×C4×C71—28no—
382C2×C4×C71—28no—
383C2×C4×C71—28no—
384C2×C4×C71—22no—
385C2×C4×C71—22no—
386C2×C4×C71—22no—
387C2×C4×C71—22no—
388C2×C4×C71—22no—
389C2×C4×C71—22no—
390C2×C4×C71—22no—
391C2×C4×C71—22no—
392C2×C4×C71—22no—
393C2×C4×C71—22no—
394C2×C4×C71—22no—
395C2×C4×C71—22no—
396C2×C4×C71—22no—
397C2×C4×C71—22no—
398C2×C4×C71—22no—
399C2×C4×C71—416no—
400C2×C4×C71—44no—
401C2×C4×C71—44no—
402C2×C4×C71—44no—
403C2×C4×C71C22×D414yes—
404C2×C4×C71C22×D414yes—
405C2×C4×C71C22×D414yes—
406C22⋊D71—416no—
407C2×Dic71—28no—
408C2×Dic71—22no—
409C2×Dic71—22no—
410C2×Dic71—22no—
411C2×Dic71—22no—
412C2×Dic71—22no—
413C2×Dic71—22no—
414C2×Dic71—22no—
415C2×Dic71—22no—
416C2×Dic71—22no—
417C2×Dic71—22no—
418C2×Dic71—22no—
419C2×Dic71—22no—
420C2×Dic71—22no—
421C2×Dic71—22no—
422C2×Dic71—416no—
423C2×Dic71—44no—
424C2×Dic71—44no—
425C2×Dic71—44no—
426C2×Dic71—44no—
427C2×Dic71C22×D414yes—
428D284—416no—
429D284—416no—
430Dic142—416no—
431C22×C71—24no—
432C22×C71—24no—
433C22×C71—24no—
434C22×C71—24no—
435C22×C71—24no—
436C22×C71—24no—
437C22×C71—232no—
438C22×C71#52514yes—
439C22×C71C2×#12414yes—
440C22×C71C2×#12418yescomplemented
441C22×C71#53814yes—
442C22×C71D4214yes—
443C22×C71#54614yes—
444C22×C71#54614yes—
445C22×C71#55114yes—
446C22×C71C23×D411yescharacteristic
447C22×C71C23×D411yescharacteristic
448C22×C71C22×#4111yescharacteristic
449C22×C71C22×#4111yescharacteristic
450C22×C71C22×#4111yescharacteristic
451C22×C71C2×H(5,𝔽2)11yescharacteristic
452C22×C71C2×H(5,𝔽2)11yescharacteristic
453C2×D71—24no—
454C2×D71—24no—
455C2×D71—24no—
456C2×D71—24no—
457C2×D71—24no—
458C2×D71—24no—
459C2×D71—464no—
460C2×D71—42no—
461C2×D71—42no—
462C2×D71—42no—
463C2×D71—42no—
464C2×D71—42no—
465C2×D71—42no—
466C2×D71—42no—
467C2×D71—42no—
468C2×D71—416no—
469C2×D71—416no—
470C2×D71—42no—
471C2×D71—42no—
472C2×D71—42no—
473C2×D71—42no—
474C2×D71—42no—
475C2×D71—42no—
476C2×D71—42no—
477C2×D71—88no—
478C4×C71—24no—
479C4×C71—24no—
480C4×C71—24no—
481C4×C71—42no—
482C4×C71—42no—
483C4×C71—42no—
484Dic71—24no—
485Dic71—42no—
486Dic71—42no—
487Dic71—42no—
488Dic71—42no—
489C2×#2472—711nomaximal, Sylow
490C2×C71—28no—
491C2×C71#247218yescomplemented
492C2×C71C2×#52511yescharacteristic
493C2×C71C22×#12411yescharacteristic
494C2×C71C2×#53811yescharacteristic
495C2×C71C2×D4211yescharacteristic
496C2×C71C2×#54611yescharacteristic
497C2×C71C2×#54611yescharacteristic
498C2×C71C2×#55111yescharacteristic
499D71—44no—
500D71—44no—
501D71—82no—
502C22×#124—711no—
503C22×C22⋊Q8—711no—
504C22×#120—711no—
505C23×C22⋊C4—711no—
506#2472—7116no—
507C2×#397—711no—
508C2×#394—711no—
509C2×#394—711no—
510C2×#393—711no—
511C2×#390—711no—
512C2×#388—711no—
513C2×#388—711no—
514C2×#386—711no—
515C2×#386—711no—
516C2×#379—711no—
517C2×C4×C22⋊C4D7111yescharacteristic, complemented
518C71C2×#247211yescharacteristic, complemented, Sylow
519C26—711no—
520C23×Q8—711no—
521C23×D4—711no—
522C23×D4—711no—
523C23×D4—711no—
524C24×C4—711no—
525C24×C4C2×D7111yescharacteristic
526C2×#124—718no—
527C2×#124—1428no—
528C2×C22⋊Q8—718no—
529C2×C22⋊Q8—1428no—
530C2×#120—718no—
531C2×#120—1428no—
532C22×C4⋊C4—711no—
533C22×C4⋊C4—711no—
534C22×C4⋊C4—711no—
535C22×C22⋊C4—711no—
536C22×C22⋊C4—711no—
537C22×C22⋊C4—711no—
538C22×C22⋊C4—711no—
539C22×C22⋊C4—711no—
540C22×C22⋊C4—711no—
541C22×C22⋊C4—711no—
542C22×C22⋊C4—711no—
543C22×C22⋊C4—711no—
544C22×C22⋊C4—711no—
545C22×C22⋊C4—711no—
546C22×C22⋊C4—711no—
547C22×C22⋊C4—711no—
548C22×C22⋊C4—711no—
549C22×C22⋊C4—718no—
550C22×C22⋊C4—711no—
551C22×C22⋊C4—1428no—
552C22×C22⋊C4C2×D7111yescharacteristic
553C22×C22⋊C4C2×D7111yescharacteristic
554C22×C42C2×D7111yescharacteristic, complemented
555C22×C42C2×D7111yescharacteristic, complemented
556#397—718no—
557#394—718no—
558#394—718no—
559#393—718no—
560#390—718no—
561#388—718no—
562#388—718no—
563#386—718no—
564#386—718no—
565#379—718no—
566C4×C22⋊C4C2×D7118yescomplemented
567C2×#95—711no—
568C2×#95—711no—
569C2×#95—711no—
570C2×#95—711no—
571C2×#95C2×D7111yescharacteristic, complemented
572C2×#95C2×D7111yescharacteristic, complemented
573C25—2842no—
574C25—2842no—
575C25—714no—
576C25—711no—
577C25—711no—
578C25—711no—
579C25—1424no—
580C25—1424no—
581C25—1424no—
582C25—1424no—
583C25—1424no—
584C25C22×D7111yescharacteristic
585C22×Q8—2842no—
586C22×Q8—714no—
587C22×Q8—1424no—
588C22×Q8—1424no—
589C22×D4—2842no—
590C22×D4—2842no—
591C22×D4—714no—
592C22×D4—714no—
593C22×D4—714no—
594C22×D4—1424no—
595C22×D4—1424no—
596C22×D4—1424no—
597C22×D4—1424no—
598C22×D4—1424no—
599C22×D4—1424no—
600C22×D4—1424no—
601C23×C4—24no—
602C23×C4—24no—
603C23×C4—42no—
604C23×C4—2842no—
605C23×C4—714no—
606C23×C4—711no—
607C23×C4—711no—
608C23×C4—711no—
609C23×C4—711no—
610C23×C4—711no—
611C23×C4—1424no—
612C23×C4—1424no—
613C23×C4C22×D7111yescharacteristic
614C23×C4C22×D7111yescharacteristic
615C23×C4C22×D7111yescharacteristic
616C23×C4C22×D7114yes—
617C23×C4C22×D7111yescharacteristic
618C23×C4C22×D7111yescharacteristic
619C23×C4C22×D7111yescharacteristic
620#124—14232no—
621C22⋊Q8—14232no—
622#120—14232no—
623C2×C4⋊C4—714no—
624C2×C4⋊C4—714no—
625C2×C4⋊C4—714no—
626C2×C4⋊C4—1424no—
627C2×C4⋊C4—1424no—
628C2×C4⋊C4—1424no—
629C2×C22⋊C4—24no—
630C2×C22⋊C4—2842no—
631C2×C22⋊C4—2842no—
632C2×C22⋊C4—2842no—
633C2×C22⋊C4—2842no—
634C2×C22⋊C4—714no—
635C2×C22⋊C4—714no—
636C2×C22⋊C4—714no—
637C2×C22⋊C4—714no—
638C2×C22⋊C4—718no—
639C2×C22⋊C4—714no—
640C2×C22⋊C4—714no—
641C2×C22⋊C4—714no—
642C2×C22⋊C4—714no—
643C2×C22⋊C4—714no—
644C2×C22⋊C4—714no—
645C2×C22⋊C4—714no—
646C2×C22⋊C4—714no—
647C2×C22⋊C4—714no—
648C2×C22⋊C4—714no—
649C2×C22⋊C4—714no—
650C2×C22⋊C4—14232no—
651C2×C22⋊C4—1424no—
652C2×C22⋊C4—1424no—
653C2×C22⋊C4—1424no—
654C2×C22⋊C4—1424no—
655C2×C22⋊C4—1424no—
656C2×C22⋊C4—1424no—
657C2×C22⋊C4—1424no—
658C2×C22⋊C4—1424no—
659C2×C22⋊C4—1424no—
660C2×C22⋊C4—1424no—
661C2×C22⋊C4D28418yes—
662C2×C22⋊C4C22×D7114yes—
663C2×C22⋊C4C22×D7114yes—
664C2×C42—24no—
665C2×C42—42no—
666C2×C42C22×D7114yescomplemented
667C2×C42C22×D7114yescomplemented
668#95—714no—
669#95—714no—
670#95—714no—
671#95—714no—
672#95C22×D7114yescomplemented
673#95C22×D7114yescomplemented
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—28416no—
679C24—28416no—
680C24—28416no—
681C24—28416no—
682C24—28416no—
683C24—2844no—
684C24—2844no—
685C24—28416no—
686C24—714no—
687C24—714no—
688C24—712no—
689C24—712no—
690C24—712no—
691C24—1428no—
692C24—1428no—
693C24—14232no—
694C24—1422no—
695C24—1428no—
696C24—1422no—
697C24—1422no—
698C24—1422no—
699C24—1422no—
700C24—1428no—
701C24—1422no—
702C24—1422no—
703C24—1422no—
704C24—1422no—
705C24—1422no—
706C24—1422no—
707C24—1428no—
708C24—1422no—
709C24—1422no—
710C24—1422no—
711C24—1422no—
712C24—1422no—
713C24—1422no—
714C24—1422no—
715C24—1422no—
716C24C2×D28414yes—
717C24#1176586514yes—
718C24#1176586514yes—
719C24C23×D7112yes—
720C24C23×D7111yescharacteristic
721C2×Q8—28416no—
722C2×Q8—2844no—
723C2×Q8—1428no—
724C2×Q8—1428no—
725C2×D4—28416no—
726C2×D4—28416no—
727C2×D4—2844no—
728C2×D4—2844no—
729C2×D4—28416no—
730C2×D4—1428no—
731C2×D4—1428no—
732C2×D4—1428no—
733C2×D4—1428no—
734C2×D4—1428no—
735C2×D4—1428no—
736C2×D4—1428no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—22no—
740C22×C4—22no—
741C22×C4—22no—
742C22×C4—22no—
743C22×C4—22no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—28no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—22no—
752C22×C4—22no—
753C22×C4—28no—
754C22×C4—44no—
755C22×C4—416no—
756C22×C4—28416no—
757C22×C4—2844no—
758C22×C4—714no—
759C22×C4—712no—
760C22×C4—712no—
761C22×C4—712no—
762C22×C4—712no—
763C22×C4—712no—
764C22×C4—1428no—
765C22×C4—1422no—
766C22×C4—1422no—
767C22×C4—1422no—
768C22×C4—1422no—
769C22×C4—1422no—
770C22×C4—1422no—
771C22×C4—1428no—
772C22×C4—1422no—
773C22×C4—1422no—
774C22×C4—1422no—
775C22×C4—1422no—
776C22×C4—1422no—
777C22×C4—1422no—
778C22×C4—1422no—
779C22×C4—1422no—
780C22×C4D4×D7114yes—
781C22×C4C2×D28414yes—
782C22×C4C2×D28414yes—
783C22×C4C23×D7112yes—
784C22×C4C23×D7112yes—
785C22×C4C23×D7112yes—
786C22×C4C23×D7112yes—
787C22×C4C23×D7112yes—
788C22×C4C23×D7112yes—
789C4⋊C4—1428no—
790C4⋊C4—1428no—
791C4⋊C4—1428no—
792C22⋊C4—28no—
793C22⋊C4—2844no—
794C22⋊C4—2844no—
795C22⋊C4—2844no—
796C22⋊C4—2844no—
797C22⋊C4—7116no—
798C22⋊C4—1428no—
799C22⋊C4—1428no—
800C22⋊C4—1428no—
801C22⋊C4—1428no—
802C22⋊C4—1428no—
803C22⋊C4—1428no—
804C22⋊C4—1428no—
805C22⋊C4—1428no—
806C22⋊C4—1428no—
807C22⋊C4—1428no—
808C22⋊C4C2×D284116yes—
809C42—28no—
810C42—44no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—28no—
816C23—28no—
817C23—28no—
818C23—28no—
819C23—28no—
820C23—28no—
821C23—28416no—
822C23—284128no—
823C23—28416no—
824C23—28416no—
825C23—28416no—
826C23—28416no—
827C23—2844no—
828C23—2844no—
829C23—2844no—
830C23—2844no—
831C23—2844no—
832C23—2844no—
833C23—2844no—
834C23—2844no—
835C23—28416no—
836C23—2844no—
837C23—2844no—
838C23—2844no—
839C23—2844no—
840C23—2844no—
841C23—2844no—
842C23—2844no—
843C23—714no—
844C23—714no—
845C23—14232no—
846C23—1422no—
847C23—1422no—
848C23—1422no—
849C23—1422no—
850C23—1422no—
851C23—1422no—
852C23—1422no—
853C23—1422no—
854C23—1422no—
855C23—1422no—
856C23—1422no—
857C23—1422no—
858C23—1422no—
859C23—1422no—
860C23—1422no—
861C23—1422no—
862C23—1422no—
863C23—1422no—
864C23—1422no—
865C23—1428no—
866C23—1428no—
867C23—1428no—
868C23—1428no—
869C23—1428no—
870C23—1428no—
871C23#14556116116yescomplemented
872C23C2×D4×D7112yes—
873C23C22×D28414yes—
874C23C22×D28412yes—
875C23#41×D7112yes—
876C23C2×#1176586514yes—
877C23C2×#1176586514yes—
878C23C2×#1176586512yes—
879C23C2×#1176586512yes—
880C23#1455617312yes—
881C23#1455617412yes—
882C23C24×D7111yescharacteristic
883Q8—28416no—
884D4—28416no—
885D4—28416no—
886D4—28416no—
887C2×C4—22no—
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—28no—
894C2×C4—28no—
895C2×C4—28no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—416no—
906C2×C4—44no—
907C2×C4—44no—
908C2×C4—44no—
909C2×C4—2844no—
910C2×C4—2844no—
911C2×C4—2844no—
912C2×C4—2844no—
913C2×C4—28416no—
914C2×C4—714no—
915C2×C4—1422no—
916C2×C4—1422no—
917C2×C4—1422no—
918C2×C4—1422no—
919C2×C4—1422no—
920C2×C4—1422no—
921C2×C4—1422no—
922C2×C4—1422no—
923C2×C4—1422no—
924C2×C4—1422no—
925C2×C4—1422no—
926C2×C4—1422no—
927C2×C4—1422no—
928C2×C4—1422no—
929C2×C4—1428no—
930C2×C4C2×D4×D7114yes—
931C2×C4C22×D28414yes—
932C2×C4C22×D28414yes—
933C22—24no—
934C22—24no—
935C22—24no—
936C22—24no—
937C22—24no—
938C22—24no—
939C22—232no—
940C22—28464no—
941C22—2842no—
942C22—2842no—
943C22—2842no—
944C22—2842no—
945C22—2842no—
946C22—2842no—
947C22—2842no—
948C22—2842no—
949C22—28416no—
950C22—28416no—
951C22—2842no—
952C22—2842no—
953C22—2842no—
954C22—2842no—
955C22—2842no—
956C22—2842no—
957C22—2842no—
958C22—5688no—
959C22—1424no—
960C22—1424no—
961C22—1424no—
962C22—1424no—
963C22—1424no—
964C22—1424no—
965C22#1798650814yes—
966C22C2×#1455611614yes—
967C22C2×#1455611618yescomplemented
968C22#1798658214yes—
969C22D4×D28414yes—
970C22#1798663914yes—
971C22#1798664414yes—
972C22#1798667314yes—
973C22C22×D4×D7111yescharacteristic
974C22C23×D28411yescharacteristic
975C22C2×#41×D7111yescharacteristic
976C22C22×#1176586511yescharacteristic
977C22C22×#1176586511yescharacteristic
978C22C2×#1455617311yescharacteristic
979C22C2×#1455617411yescharacteristic
980C4—24no—
981C4—24no—
982C4—24no—
983C4—42no—
984C4—42no—
985C4—42no—
986C4—2842no—
987C4—2842no—
988C4—2842no—
989C4—2842no—
990C4—1424no—
991C2—28no—
992C2—2844no—
993C2—2844no—
994C2—5682no—
995C2#2259246618yesdirect product factor
996C2C2×#1798650811yescharacteristic
997C2C22×#1455611611yescharacteristic
998C2C2×#1798658211yescharacteristic
999C2C2×D4×D28411yescharacteristic
1000C2C2×#1798663911yescharacteristic
1001C2C2×#1798664411yescharacteristic
1002C2C2×#1798667311yescharacteristic
subgroupG/H
centerC24C23×D71
commutator, cosocleC23×C71C25
FrattiniC23C24×D71
FittingC2×C4×C22⋊C4×C71C2
socleC24×C71C24
prime radicalC22×#14556098C2
hypercenterC2×C4×C22⋊C4D71
hypocenterC71C2×#2472
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#14556116C2semidirect
2. C22×#14556105C2semidirect
4. C23×(C2×D71)⋊C4C2semidirect
5. #22592466C2direct (N × H)
6. C2×#17985926C2semidirect
7. C2×#17985917C2semidirect
8. C2×#17985917C2semidirect
9. C2×#17985912C2semidirect
10. C2×#17985901C2semidirect
11. C2×#17985890C2semidirect
12. C2×#17985890C2semidirect
13. C2×#17985878C2semidirect
14. C2×#17985876C2semidirect
15. C2×#17985854C2semidirect
16. C2×C4×C22⋊C4×C71C2semidirect
18. C23×Dic142C22semidirect
24. C2×#14556116C22semidirect
26. C2×#14556105C22semidirect
29. C22×C4⋊Dic71C22semidirect
30. C22×Dic71⋊C4C22semidirect
31. C22×Dic71⋊C4C22semidirect
44. C22×(C2×D71)⋊C4C22semidirect
45. C22×(C2×D71)⋊C4C22semidirect
46. C22×(C2×D71)⋊C4C22semidirect
47. C22×(C2×D71)⋊C4C22semidirect
48. C22×(C2×D71)⋊C4C22semidirect
49. #17985926C22semidirect
50. #17985917C22semidirect
51. #17985917C22semidirect
52. #17985912C22semidirect
53. #17985901C22semidirect
54. #17985890C22semidirect
55. #17985890C22semidirect
56. #17985878C22semidirect
57. #17985876C22semidirect
58. #17985854C22semidirect
59. C2×C71⋊#95C22semidirect
60. C2×C71⋊#95C22semidirect
61. C2×C71⋊#95C22semidirect
62. C2×C71⋊#95C22semidirect
66. C22×C42×C71C22semidirect
67. C22×C42×C71C22semidirect
68. C4×C22⋊C4×C71C22semidirect
69. C2×#95×C71C22semidirect
70. C2×#95×C71C22semidirect
85. C22×Dic142C23semidirect
111. C2×C4⋊Dic71C23semidirect
114. C2×Dic71⋊C4C23semidirect
115. C2×Dic71⋊C4C23semidirect
132. C2×(C2×D71)⋊C4D4semidirect
143. C2×(C2×D71)⋊C4C23semidirect
144. C2×(C2×D71)⋊C4C23semidirect
145. C2×(C2×D71)⋊C4C23semidirect
146. C2×(C2×D71)⋊C4C23semidirect
147. C71⋊#95C23semidirect
148. C71⋊#95C23semidirect
149. C71⋊#95C23semidirect
150. C71⋊#95C23semidirect
168. C2×C42×C71C23semidirect
169. C2×C42×C71C23semidirect
170. #95×C71C23semidirect
171. #95×C71C23semidirect
267. (C2×D71)⋊C4C2×D4semidirect
319. C23×C71#124semidirect
440. C22×C71C2×#124semidirect
491. C2×C71#2472semidirect
517. C2×C4×C22⋊C4D71semidirect
518. C71C2×#2472semidirect
554. C22×C42C2×D71semidirect
555. C22×C42C2×D71semidirect
566. C4×C22⋊C4C2×D71semidirect
571. C2×#95C2×D71semidirect
572. C2×#95C2×D71semidirect
666. C2×C42C22×D71semidirect
667. C2×C42C22×D71semidirect
672. #95C22×D71semidirect
673. #95C22×D71semidirect
871. C23#14556116semidirect
967. C22C2×#14556116semidirect
995. C2#22592466direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#145561162
C22×#145561052
C22×#145560982
C23×(C2×D71)⋊C42
#225924662
C2×#179859262
C2×#179859172
C2×#179859122
C2×#179859012
C2×#179858902
C2×#179858782
C2×#179858762
C2×#179858542
C2×C4×C22⋊C4×C712
C2×#247271